{"paper":{"title":"Radial Projections in $\\mathbb{R}^n$ Revisited","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.CA","authors_text":"Kevin Ren, Paige Bright, Yuqiu Fu","submitted_at":"2024-06-14T04:24:49Z","abstract_excerpt":"We generalize the recent results on radial projections by Orponen, Shmerkin, Wang using two different methods. In particular, we show that given $X,Y\\subset \\mathbb{R}^n$ Borel sets and $X\\neq \\emptyset$. If $\\dim Y \\in (k,k+1]$ for some $k\\in \\{1,\\dots, n-1\\}$, then \\[ \\sup_{x\\in X} \\dim \\pi_x(Y\\setminus \\{x\\}) \\geq \\min \\{\\dim X + \\dim Y - k, k\\}. \\] Our results give a new approach to solving a conjecture of Lund-Pham-Thu in all dimensions and for all ranges of $\\dim Y$.\n  The first of our two methods for proving the above theorem is shorter, utilizing a result of the first author and Gan. O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09707","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.09707/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}